Abo Bibliothek: Guest
Digitales Portal Digitale Bibliothek eBooks Zeitschriften Referenzen und Berichte Forschungssammlungen
Multiphase Science and Technology
SJR: 0.124 SNIP: 0.222 CiteScore™: 0.26

ISSN Druckformat: 0276-1459
ISSN Online: 1943-6181

Multiphase Science and Technology

DOI: 10.1615/MultScienTechn.2019028624
pages 73-85


Avick Sinha
Indian Institute of Technology Bombay, Mumbai, India, 400076
Shivasubramanian Gopalakrishnan
Indian Institute of Technology Bombay, Mumbai, India, 400076


The aim of this effort is to employ the homogeneous relaxation model to study thermal nonequilibrium in flash boiling flows. The use of convergent-divergent nozzles is prevalent in geothermal total flow systems for power generation, and the understanding of the physics of two-phase flows in such systems is of primary importance to achieve greater efficiencies. Most numerical studies for such nonequilibrium phase-change models have used one dimensional approaches, but the objective of the present work is to utilize a multidimensional computational fluid dynamics implementation for such complex flows. It was observed that the slip between the vapor and liquid along the divergent section of the nozzle and the maximum nonequilibrium pressure drop at the nozzle throat due to the thermal nonequilibrium causes an increase in the nozzle efficiency with the decrease in back pressure. The model was validated against experimental measurements and it was observed that the simulations are in good agreement with the multidimensional features observed in the experiments.


  1. Abuaf, N., Wu, B., Zimmer, G., and Saha, P., Study of Nonequilibrium Flashing of Water in a Converging- Diverging Nozzle, Vol. 1: Experimental, Brookhaven National Laboratory, Upton, NY, Tech. Rep. NUREG/CR-1864-Vol. 1; BNL-NUREG-51317-Vol. 1, 1981.

  2. Aguilar, F. and Thompson, S., Nonequilibrium Flashing Model for Rapid Pressure Transients, Paper Presented at the 20th National Heat Transfer Conf., Milwaukee, WI, Aug. 2, 1981.

  3. Akagawa, K., Fujii, T., Ohta, J., and Takagi, S., Cycle Performance of Total Flow Turbine Systems: 1st Report, Utilization of Saturated Hot Water, JSME Int. J. Bulletin JSME, vol. 30, no. 262, p. 692, 1987.

  4. Akagawa, K., Fujii, T., Ohta, J., Takenaka, N., and Taniguchi, K., Performance Characteristics of Convergent-Divergent Nozzles for Subcooled Hot Water (2nd Report, Improvement of Nozzle Performance), Trans. Japan Soc. Mech. Eng. Ser. B, vol. 55, no. 517, pp. 2743–2750, 1989.

  5. Austin, A. and Lundberg, A., A Comparison of Methods for Electric Power Generation from Geothermal Hot Water Deposits, ASME Paper No. 74-WA, 1974.

  6. Bilicki, Z. and Kestin, J., Physical Aspects of the Relaxation Model in Two-Phase Flow, Proc. R. Soc. London Ser. A, vol. 428, pp. 379–397, 1990.

  7. Boure, J., Fritte, A., Giot, M., and Reocreux, M., Highlights of Two-Phase Critical Flow: On the Links between Maximum Flow Rates, Sonic Velocities, Propagation and Transfer Phenomena in Single and Two-Phase Flows, Int. J. Multiphase Flow, vol. 3, no. 1, pp. 1–22, 1976.

  8. Downar-Zapolski, P., Bilicki, Z., Bolle, L., and Franco, J., The Non-Equilibrium Relaxation Model for One-Dimensional Flashing Liquid Flow, Int. J. Multiphase Flow, vol. 22, no. 3, pp. 473–483, 1996.

  9. Fauske, H., The Discharge of Saturated Water through Tubes, Chem. Eng. Prog. Symp. Ser., vol. 61, pp. 210–216, 1965.

  10. Ferziger, J.H., Peric, M., and Leonard, A., Computational Methods for Fluid Dynamics, Berlin, Germany: Springer Science & Business Media, 1997.

  11. Henry, D.R.E. and Fauske, H.K., The Two-Phase Critical Flow of One-Component Mixtures in Nozzles, Orifices, and Short Tubes, New York: ASME, 1970.

  12. Isbin, H., Moy, J., and Da Cruz, A., Two-Phase, Steam-Water Critical Flow, AIChE J., vol. 3, no. 3, pp. 361–365, 1957.

  13. Jasak, H., Weller, H., and Gosman, A., High Resolution NVD Differencing Scheme for Arbitrarily Unstructured Meshes, Int. J. Num. Methods Fluids, vol. 31, no. 2, pp. 431–449, 1999.

  14. Kato, H., Kayano, H., and Kageyama, Y., A Consideration of Thermal Effect on Cavitation Bubble Growth, American Society of Mechanical Engineers, New York, NY, Tech. Rep. CONF-940659, 1994.

  15. Lamanna, G., Kamoun, H., Weigand, B., and Steelant, J., Towards a Unified Treatment of Fully Flashing Sprays, Int. J. Multiphase Flow, vol. 58, pp. 168–184, 2014.

  16. Lemmon, E.W., Huber, M.L., and McLinden, M.O., NIST Reference Fluid Thermodynamic and Transport Properties (REFPROP), NIST Stand. Ref. Database, vol. 23, p. v7, 2002.

  17. Linning, D.L., The Adiabatic Flow of Evaporating Fluids in Pipes of Uniform Bore, Proc. Instit. Mech. Eng., Part B, vol. 1, nos. 1-12, pp. 64–75, 1953.

  18. Maneely, D., A Study of the Expansion Process of Low-Quality Steam through a de Laval Nozzle, PhD Thesis, California University, 1962.

  19. Massena, W., Steam-Water Critical Flow using the “Separated Flow Model,” General Electric Co. Hanford Atomic Products Operation, Richland, WA, Tech. Rep. HW-65739, 1960.

  20. Mutair, S. and Ikegami, Y., Experimental Investigation on the Characteristics of Flash Evaporation from Superheated Water Jets for Desalination, Desalination, vol. 251, no. 1, pp. 103–111, 2010.

  21. Neusen, K., Optimizing of Flow Parameters for the Expansion of Very Low-Quality Steam, PhD Thesis, California University, 1962.

  22. Ohta, J., Fujii, T., Akagawa, K., and Takenaka, N., Performance and Flow Characteristics of Nozzles for Initially Subcooled Hot Water (Influence of Turbulence and Decompression Rate), Int. J. Multiphase Flow, vol. 19, no. 1, pp. 125–136, 1993.

  23. Polanco, G., Holdø, A.E., and Munday, G., General Review of Flashing Jet Studies, J. Hazard. Mate., vol. 173, nos. 1-3, pp. 2–18, 2010.

  24. Reitz, R.D., A Photographic Study of Flash-Boiling Atomization, Aerosol Sci. Technol., vol. 12, no. 3, pp. 561–569, 1990.

  25. Schmidt, D., Gopalakrishnan, S., and Jasak, H., Multi-Dimensional Simulation of Thermal Non- Equilibrium Channel Flow, Int. J. Multiphase Flow, vol. 36, no. 4, pp. 284–292, 2010.

  26. Schmidt, D.P., Rutland, C.J., and Corradini, M.L., A Fully Compressible, Two-Dimensional Model of Small, High-Speed, Cavitating Nozzles, Atom. Sprays, vol. 9, no. 3, pp. 255–276, 1999.

  27. Senda, J., Hojyo, Y., and Fujimoto, H., Modeling on Atomization and Vaporization Process in Flash Boiling Spray, JSAE Rev., vol. 15, no. 4, pp. 291–296, 1994.

  28. Senocak, I. and Shyy, W., A Pressure-based Method for Turbulent Cavitating Flow Computations, J. Comput. Phys., vol. 176, no. 2, pp. 363–383, 2002.

  29. Sher, E., Bar-Kohany, T., and Rashkovan, A., Flash-Boiling Atomization, Prog. Energy Combust. Sci., vol. 34, no. 4, pp. 417–439, 2008.

  30. Simoneau, R.J., Pressure Distribution in a Converging-Diverging Nozzle during Two-Phase Choked Flow of Subcooled Nitrogen, Winter Ann. Meeting of the Am. Soc. of Mech. Eng., December, 1975.

  31. Sinha, A., Chauhan, R.O., and Balasubramanian, S., Characterization of a Superheated Water Jet Released into Water using Proper Orthogonal Decomposition Method, J. Fluids Eng., vol. 140, no. 8, p. 081107, 2018.

  32. Sozzi, G.L. and Sutherland, W.A., Critical Flow of Saturated and Subcooled Water at High Pressure, General Electric Co., San Jose, CA, Boiling Water Reactor Systems Dept., Rep. NEDO-13418, 1975.

  33. Starkman, E. and Brown, R., Flashing Flow of Initially SubcooledWater in Convergent-Divergent Nozzles, J. Heat Trans., vol. 20, p. 40, 1977.

  34. Vahaji, S., Akbarzadeh, A., Date, A., Cheung, C., and Tu, J., Study on the Efficiency of a Convergent-Divergent Two-Phase Nozzle as a Motive Force for Power Generation from Low Temperature Geothermal Resources, World Gas Conf. 2015: Views from Down Under-Geothermal in Perspective, Arinex Pty Ltd., pp. 1–14, 2015.

  35. Valero, E. and Parra, I., The Role of Thermal Disequilibrium in Critical Two-Phase Flow, Int. J. Multiphase Flow, vol. 28, no. 1, pp. 21–50, 2002.

  36. Wallis, G.B., Critical Two-Phase Flow, Int. J. Multiphase Flow, vol. 6, nos. 1-2, pp. 97–112, 1980.

  37. Weller, H.G., Tabor, G., Jasak, H., and Fureby, C., A Tensorial Approach to Computational Continuum Mechanics using Object-Oriented Techniques, Comput. Phys., vol. 12, no. 6, pp. 620–631, 1998.

  38. Zeng, Y. and Lee, C.F.F., An Atomization Model for Flash Boiling Sprays, Combust. Sci. Technol., vol. 169, no. 1, pp. 45–67, 2001.